Question

hi! im mia, and i need help with math!question: Write a statement that correctly describes the relationship between these two sequences: 6, 7, 8, 9, 10, and 18, 21, 24, 27, 30.

Answer 1

The Solution:

Given the pair of sequences below:

`\begin{gathered} \text{ First sequence: 6,7,8,9,10} \\ \\ \text{ Second sequence: 18,21,24,27,30} \end{gathered}`

We are asked to write a statement that correctly describes the relationship between the two sequences.

The two sequences are both linear sequences. Their common differences are:

`\begin{gathered} \text{ First sequence: d=T}_3-T_2=\text{T}_2-T_1 \\ =8-7=7-6=1 \\ \text{ So, the co}mmon\text{ difference is 1} \end{gathered}`

The general formula for the first sequence is

`T_n=a+(n-1_{})d=6+(n_{}-1)1=6+n-1=5+n`

Similarly,

`\begin{gathered} \text{ Second sequence}\colon\text{ } \\ d=\text{T}_3-T_2=\text{T}_2-T_1 \\ d=24-21=21-18=3 \\ \text{ So, the co}mmon\text{ difference is 3} \end{gathered}`

The general formula for the second sequence is

`S_n=18+(n-1_{})3=18+3n_{}-3=15+3n=3(5+n)`

Thus, the relationship between the two sequences is:

`S_n=3T_n`

Where

`\begin{gathered} S_n=\text{ the second sequence} \\ T_n=\text{ the first sequence} \end{gathered}`

Therefore, the correct answer is:

`S_n=3T_n`